The Dielectric Tensor for Magnetized Dusty Plasmas with Superthermal Plasma Populations and Dust Particles of Different Sizes

Abstract

We present general expressions for the components of the dielectric tensor of magnetized dusty plasmas, valid for arbitrary direction of propagation and for situations in which populations of dust particles of different sizes are present in the plasma. These expressions are derived using a kinetic approach which takes into account the variation of the charge of the dust particles due to inelastic collisions with electrons and ions, and features the components of the dielectric tensor in terms of a finite and an infinite series, containing all effects of harmonics and Larmor radius, and is valid for the whole range of frequencies above the plasma frequency of the dust particles, which are assumed to be motionless. The integrals in velocity space which appear in the dielectric tensor are solved assuming that the electron and ion populations are described by anisotropic non-thermal distributions characterized by parameters κ and κ ⊥ , featuring the Maxwellian as a limiting case. These integrals can be written in terms of generalized dispersion functions, which can be expressed in terms of hypergeometric functions. The formulation therefore becomes specially suitable for numerical analysis.

Kinetic theory of magnetized dusty plasmas with dust particles charged by collisional processes and by photoionization

“…In our model, we consider that there are n dust populations characterized by different radius a j and electric charge q j . 4 The dielectric tensor will be derived in the scope of kinetic theory, approach which has already been used to demonstrate that effects due to the dust charging can lead to significant modification in the damping of low frequency waves. 11 Our approach is based on previous works of Vladimirov 24 and of de Juli and Schneider, 8 from which we follow the collisional model and make the necessary modifications to include photoionization effects.…”

“…(52) and (58), the contribution to the plasma dielectric tensor which is associated with f A ak can be written more conveniently as a product of two dimensionless vector quantities 4 A ij ¼ 4pi…”

Alfvén waves in dusty plasmas with plasma particles described by anisotropic kappa distributions

“…However, for the present application, we will neglect the "new" contribution, as in previous analysis of the dispersion relation for Alfv en waves. 34,35,43 The point is that the "new" contributions contain integrals over velocity variables that are similar to those of the "conventional" contributions, but multiplied by the small ratio between the frequency of collisions with dust particles and a characteristic frequency, which is assumed as the ion cyclotron frequency in the case of Alfv en waves. In another example, in the case of electrostatic waves, it has already been shown that the effect of the "new" contribution is negligible, for small population of dust particles.…”

“…Distribution (11), which is also called "product bi-kappa" distribution, has been utilized in a recent paper presenting a detailed derivation of the components of the dielectric tensor of a dusty plasma and a detailed calculation of the velocity integrals depending on the equilibrium velocity distributions, which appear in these components. 43 As it is known, the Maxwellian distribution is the limiting case of kappa distributions when the parameter j becomes sufficiently large. In Figure 1, we show contour plots for four different forms of the distribution function, vs. …”

Obliquely propagating electromagnetic waves in magnetized kappa plasmas

“…24,25 Finally, it has been also observed that in a dusty plasma, the excess of superthermal plasma particles affects not only the wave-resonance characteristics (dispersion relations and damping/growth rates), but alters the resulting electrical charge of the dust particles as well. [26][27][28][29][30][31] Some theories have been proposed to address the origin of κVDFs from a fundamental set of postulates. The most accepted explanation nowadays is based on the principle of nonadditive entropy proposed by C. Tsallis.…”